NeuraNet - Master Neural Networks from Beginner to Advanced

Fundamentals

Neural Network Basics

Understanding the fundamental building blocks of neural networks

1 The Perceptron - Building Block

The perceptron is the simplest form of a neural network, consisting of a single neuron. It was invented by Frank Rosenblatt in 1958 and laid the foundation for modern neural networks.

Perceptron Function

y = f(w₁x₁ + w₂x₂ + ... + wₙxₙ + b)

Where:
• y = Output (prediction/result)
• f = Activation function (introduces non-linearity)
• w₁, w₂, ..., wₙ = Weights (learnable parameters)
• x₁, x₂, ..., xₙ = Input features
• n = Number of input features
• b = Bias term (offset value)

Components:

Inputs (x): Features or attributes fed into the neuron
Weights (w): Parameters that determine the importance of each input
Bias (b): Offset value that helps the model fit the data better
Activation Function (f): Introduces non-linearity to the model
Output (y): Final prediction or classification

2 Activation Functions

Activation functions introduce non-linearity into the network, enabling it to learn complex patterns. Without activation functions, neural networks would only be able to learn linear relationships.

Sigmoid

σ(x) = 1 / (1 + e⁻ˣ)

Where: σ = Sigma (sigmoid function), x = Input value, e = Euler's number (≈2.718)

Range: (0, 1)

Use Case: Binary classification, output layer

Pros: Smooth gradient, clear predictions

Cons: Vanishing gradient problem, not zero-centered

Tanh (Hyperbolic Tangent)

tanh(x) = (eˣ - e⁻ˣ) / (eˣ + e⁻ˣ)

Where: x = Input value, e = Euler's number (≈2.718), eˣ = e raised to power x

Range: (-1, 1)

Use Case: Hidden layers in RNNs

Pros: Zero-centered, stronger gradients than sigmoid

Cons: Still suffers from vanishing gradient

ReLU (Rectified Linear Unit)

ReLU(x) = max(0, x)

Where: x = Input value, max = Maximum function (returns 0 if x<0, else returns x)

Range: [0, ∞]

Use Case: Most popular for hidden layers

Pros: Computationally efficient, no vanishing gradient

Cons: Dead neurons problem

Leaky ReLU

f(x) = max(αx, x)

Where: x = Input value, α = Small positive constant (typically 0.01), max = Maximum function

Range: (-∞, ∞)

Use Case: Alternative to ReLU

Pros: Prevents dead neurons, allows small negative values

Cons: Inconsistent predictions for negative values

Softmax

σ(x)ᵢ = eˣⁱ / Σⱼ eˣʲ

Where: σ(x)ᵢ = Softmax output for class i, xᵢ = Input for class i, e = Euler's number, Σⱼ = Sum over all classes j

Range: (0, 1), sum = 1

Use Case: Multi-class classification output

Pros: Probability distribution, interpretable

Cons: Computational overhead

ELU (Exponential Linear Unit)

f(x) = x if x > 0, α(eˣ - 1) if x ≤ 0

Where: x = Input value, α = Hyperparameter (typically 1.0), e = Euler's number (≈2.718)

Range: (-α, ∞)

Use Case: Deep networks

Pros: Smooth, zero-centered, reduces bias shift

Cons: More computation than ReLU

3 Weights and Biases

Weights (w)

Weights are the learnable parameters that determine the strength of connections between neurons. They control how much influence each input has on the output.

Initialization: Proper weight initialization is crucial (Xavier, He, Random)
Learning: Weights are adjusted during training through backpropagation
Impact: Larger weights mean stronger influence on the output
Regularization: Techniques like L1/L2 prevent weights from becoming too large

Biases (b)

Bias is an additional parameter that allows the activation function to be shifted left or right, helping the model fit the data better.

Purpose: Provides flexibility in fitting the data
Independence: Unlike weights, bias is not multiplied by input
Initialization: Usually initialized to zero or small values
Role: Helps the model make predictions even when all inputs are zero

Weight Matrix Representation

In matrix form, the operation of a layer can be represented as:

Y = f(W·X + B)

Where:
• Y = Output vector (results from the layer)
• f = Activation function
• W = Weight matrix (learnable parameters)
• X = Input vector (features)
• B = Bias vector (offset terms)
• · = Matrix multiplication

Structure

Neural Network Architecture

Exploring the layers and structure of neural networks

4 Network Layers

Input Layer

The first layer that receives raw data. Each neuron represents one feature of the input data.

Number of neurons = number of features
No computation, just passes data forward
Example: 784 neurons for 28x28 pixel image

Hidden Layers

Intermediate layers that perform computations and extract features. The "deep" in deep learning refers to multiple hidden layers.

Can have multiple hidden layers
Each layer learns different level of abstraction
First layers: simple features (edges, colors)
Deeper layers: complex features (faces, objects)

OUT

Output Layer

The final layer that produces predictions. Number of neurons depends on the task.

Binary classification: 1 neuron (sigmoid)
Multi-class: n neurons (softmax)
Regression: 1 or more neurons (linear)

5 Forward Propagation

Forward propagation is the process of passing input data through the network to generate an output. It's called "forward" because data flows from input to output.

Step-by-Step Process:

Input Layer: Receive input data
a⁽⁰⁾ = X
Where: a⁽⁰⁾ = Activation at layer 0, X = Input data
Hidden Layer Computation: For each layer l
z⁽ˡ⁾ = W⁽ˡ⁾·a⁽ˡ⁻¹⁾ + b⁽ˡ⁾ a⁽ˡ⁾ = f(z⁽ˡ⁾)
Where: z⁽ˡ⁾ = Pre-activation at layer l, W⁽ˡ⁾ = Weights at layer l, a⁽ˡ⁻¹⁾ = Activation from previous layer, b⁽ˡ⁾ = Bias at layer l, a⁽ˡ⁾ = Activation at layer l, f = Activation function
Output Layer: Final prediction
ŷ = a⁽ᴸ⁾
Where: ŷ = Predicted output, a⁽ᴸ⁾ = Activation at final layer L, L = Total number of layers
Loss Calculation: Compare prediction with actual
Loss = L(ŷ, y)
Where: L = Loss function, ŷ = Predicted output, y = Actual target value

Key Terms:

z: Pre-activation (weighted sum + bias)
a: Activation (after applying activation function)
W: Weight matrix
b: Bias vector
l: Layer number

Input

x₁

x₂

x₃

→

Hidden 1

h₁

h₂

h₃

h₄

→

Hidden 2

h₁

h₂

h₃

→

Output

6 Network Depth and Width

Shallow Networks

Networks with few hidden layers (1-2 layers)

✓ Faster to train
✓ Less prone to overfitting
✓ Easier to debug
✗ Limited learning capacity
✗ Can't learn complex patterns

Best for: Simple problems, small datasets

Deep Networks

Networks with many hidden layers (3+ layers)

✓ Learn hierarchical features
✓ Better for complex tasks
✓ State-of-the-art performance
✗ Requires more data
✗ Longer training time
✗ Risk of overfitting

Best for: Complex problems, large datasets

Wide Networks

Networks with many neurons per layer

✓ More parameters to learn
✓ Better feature representation
✗ More memory required
✗ Slower computation
✗ Risk of overfitting

Best for: High-dimensional data

Learning

Training Neural Networks

Understanding how neural networks learn from data

7 Backpropagation Algorithm

Backpropagation is the cornerstone of neural network training. It efficiently computes gradients of the loss function with respect to all weights in the network using the chain rule of calculus.

How It Works:

Forward Pass: Compute predictions and loss
Compute Output Gradient:
∂L/∂a⁽ᴸ⁾ = ∂L/∂ŷ
Where: ∂L/∂a⁽ᴸ⁾ = Gradient of loss w.r.t. output activation, L = Loss, a⁽ᴸ⁾ = Output layer activation, ŷ = Prediction
Backward Pass: For each layer from L to 1
∂L/∂z⁽ˡ⁾ = ∂L/∂a⁽ˡ⁾ · f'(z⁽ˡ⁾) ∂L/∂W⁽ˡ⁾ = ∂L/∂z⁽ˡ⁾ · (a⁽ˡ⁻¹⁾)ᵀ ∂L/∂b⁽ˡ⁾ = ∂L/∂z⁽ˡ⁾ ∂L/∂a⁽ˡ⁻¹⁾ = (W⁽ˡ⁾)ᵀ · ∂L/∂z⁽ˡ⁾
Where: ∂ = Partial derivative, L = Loss, z⁽ˡ⁾ = Pre-activation at layer l, a⁽ˡ⁾ = Activation at layer l, f' = Derivative of activation function, W⁽ˡ⁾ = Weights at layer l, b⁽ˡ⁾ = Bias at layer l, ᵀ = Transpose, · = Matrix multiplication
Update Weights: Using gradients
W⁽ˡ⁾ = W⁽ˡ⁾ - α · ∂L/∂W⁽ˡ⁾ b⁽ˡ⁾ = b⁽ˡ⁾ - α · ∂L/∂b⁽ˡ⁾
Where: W⁽ˡ⁾ = Updated weights, α = Learning rate (step size), ∂L/∂W⁽ˡ⁾ = Gradient of loss w.r.t. weights, b⁽ˡ⁾ = Updated bias, ∂L/∂b⁽ˡ⁾ = Gradient of loss w.r.t. bias

Chain Rule in Action:

Backpropagation applies the chain rule to propagate errors from output to input:

∂L/∂W⁽¹⁾ = ∂L/∂a⁽ᴸ⁾ · ∂a⁽ᴸ⁾/∂z⁽ᴸ⁾ · ... · ∂a⁽¹⁾/∂z⁽¹⁾ · ∂z⁽¹⁾/∂W⁽¹⁾

Where: Each partial derivative represents the gradient at that layer, chained together from output (L) to first layer (1) using the chain rule from calculus

8 Loss Functions

Loss functions measure how well the network's predictions match the actual values. The goal of training is to minimize this loss.

Mean Squared Error (MSE)

MSE = (1/n) Σ(yᵢ - ŷᵢ)²

Where: n = Number of samples, Σ = Sum, yᵢ = Actual value for sample i, ŷᵢ = Predicted value for sample i, ² = Squared (power of 2)

Use Case: Regression problems

Characteristics:

Penalizes large errors heavily
Always positive
Differentiable everywhere

Binary Cross-Entropy

BCE = -1/n Σ[yᵢlog(ŷᵢ) + (1-yᵢ)log(1-ŷᵢ)]

Where: n = Number of samples, Σ = Sum, yᵢ = Actual label (0 or 1), ŷᵢ = Predicted probability, log = Natural logarithm

Use Case: Binary classification

Characteristics:

Measures probability distribution distance
Works with sigmoid activation
Penalizes confident wrong predictions

Categorical Cross-Entropy

CCE = -Σᵢ Σⱼ yᵢⱼ log(ŷᵢⱼ)

Where: Σᵢ = Sum over all samples i, Σⱼ = Sum over all classes j, yᵢⱼ = Actual label for sample i and class j (one-hot encoded), ŷᵢⱼ = Predicted probability, log = Natural logarithm

Use Case: Multi-class classification

Characteristics:

Works with softmax activation
Handles multiple classes
One-hot encoded targets

Mean Absolute Error (MAE)

MAE = (1/n) Σ|yᵢ - ŷᵢ|

Where: n = Number of samples, Σ = Sum, yᵢ = Actual value for sample i, ŷᵢ = Predicted value for sample i, | | = Absolute value

Use Case: Regression with outliers

Characteristics:

Less sensitive to outliers than MSE
Linear penalty for errors
More robust

9 Optimization Algorithms

Optimization algorithms determine how the network updates its weights to minimize the loss function.

Gradient Descent (GD)

θ = θ - α · ∇J(θ)

Where: θ = Parameters (weights & biases), α = Learning rate, ∇J(θ) = Gradient of cost function J w.r.t. parameters θ, · = Multiplication

The basic optimization algorithm that updates weights using the gradient of the entire dataset.

✓ Stable convergence
✓ Guaranteed to converge (convex problems)
✗ Slow for large datasets
✗ Requires full dataset per update

Stochastic Gradient Descent (SGD)

θ = θ - α · ∇J(θ; xᵢ, yᵢ)

Where: θ = Parameters, α = Learning rate, ∇J(θ; xᵢ, yᵢ) = Gradient computed on single example (xᵢ, yᵢ), xᵢ = Single input sample, yᵢ = Single target value

Updates weights using one training example at a time, making it much faster.

✓ Fast updates
✓ Can escape local minima
✓ Works with large datasets
✗ Noisy convergence
✗ Requires learning rate tuning

Mini-Batch SGD

θ = θ - α · ∇J(θ; Xᵇᵃᵗᶜʰ)

Where: θ = Parameters, α = Learning rate, ∇J(θ; Xᵇᵃᵗᶜʰ) = Gradient computed on a mini-batch, Xᵇᵃᵗᶜʰ = Small subset of training data (batch)

Balances GD and SGD by using small batches (typically 32-256 examples).

✓ Balance speed and stability
✓ Efficient computation (GPU)
✓ Most commonly used

Momentum

v = βv + α·∇J(θ) θ = θ - v

Where: v = Velocity (momentum term), β = Momentum coefficient (typically 0.9), α = Learning rate, ∇J(θ) = Gradient, θ = Parameters

Accumulates a velocity vector in directions of persistent gradient reduction.

✓ Faster convergence
✓ Dampens oscillations
✓ Escapes plateaus better

Adam (Adaptive Moment)

m = β₁m + (1-β₁)∇J(θ) v = β₂v + (1-β₂)(∇J(θ))² θ = θ - α·m/√(v+ε)

Where: m = First moment (mean of gradients), β₁ = First moment decay (typically 0.9), v = Second moment (variance of gradients), β₂ = Second moment decay (typically 0.999), ∇J(θ) = Gradient, θ = Parameters, α = Learning rate, √ = Square root, ε = Small constant (10⁻⁸) for numerical stability

Combines momentum and adaptive learning rates. Currently most popular optimizer.

✓ Works well in practice
✓ Adaptive learning rates
✓ Requires little tuning
✓ Good default choice

RMSprop

v = βv + (1-β)(∇J(θ))² θ = θ - α·∇J(θ)/√(v+ε)

Where: v = Moving average of squared gradients, β = Decay rate (typically 0.9), ∇J(θ) = Gradient, θ = Parameters, α = Learning rate, √ = Square root, ε = Small constant (10⁻⁸) for numerical stability

Adapts learning rate by dividing by exponentially decaying average of squared gradients.

✓ Good for RNNs
✓ Handles non-stationary objectives
✓ Works well on noisy data

10 Hyperparameters

Hyperparameters are configuration settings that control the training process but are not learned from data.

Learning Rate

Controls how much to change weights in response to error.

Typical Range: 0.0001 - 0.1

Too high: Training unstable, diverges
Too low: Training very slow
Solution: Learning rate scheduling

Batch Size

Number of training examples in one forward/backward pass.

Typical Range: 16 - 512

Larger: More stable gradients, faster computation
Smaller: More noise, better generalization
Common values: 32, 64, 128, 256

Epochs

Number of complete passes through the training dataset.

Typical Range: 10 - 1000

Too few: Underfitting
Too many: Overfitting
Use early stopping to find optimal

Hidden Units

Number of neurons in each hidden layer.

Typical Range: 16 - 1024

More units: More capacity to learn
Fewer units: Less prone to overfitting
Often use powers of 2

Number of Layers

Depth of the neural network.

Typical Range: 2 - 100+

More layers: Learn complex hierarchies
Deeper networks: Require more data
Start shallow, increase if needed

Regularization

Penalty term to prevent overfitting.

Typical Range: 0.0001 - 0.1

L1: Sparse weights
L2: Small weights
Dropout: Random neuron deactivation

11 Training Techniques

Batch Normalization

Normalizes inputs of each layer to have mean 0 and variance 1.

x̂ = (x - μ) / √(σ² + ε)

Benefits:

Faster training
Allows higher learning rates
Reduces internal covariate shift
Acts as regularization

Dropout

Randomly deactivates neurons during training to prevent overfitting.

How it works: With probability p, set neuron output to 0

Benefits:

Prevents co-adaptation of neurons
Acts like ensemble learning
Simple yet effective
Typical p: 0.2 - 0.5

Early Stopping

Stop training when validation performance stops improving.

Process:

Monitor validation loss
Keep best model checkpoint
Stop if no improvement for n epochs
Prevents overfitting

Data Augmentation

Artificially increase training data by applying transformations.

Techniques:

Rotation, flipping, cropping (images)
Adding noise
Color jittering
Improves generalization

Learning Rate Scheduling

Adjust learning rate during training for better convergence.

Strategies:

Step decay: Reduce by factor every n epochs
Exponential decay: Multiply by constant < 1
Cosine annealing: Follow cosine curve
Warm restarts: Periodic resets

Weight Initialization

Proper initialization prevents vanishing/exploding gradients.

Methods:

Xavier/Glorot: For sigmoid/tanh
He initialization: For ReLU
Random normal with proper variance
Critical for deep networks

Architectures

Types of Neural Networks

Different architectures for different problems

🔄

Feedforward Neural Networks (FNN)

The simplest type where information flows in one direction from input to output.

Architecture:

No cycles or loops
Information flows forward only
Fully connected layers

Applications:

Classification tasks
Regression problems
Pattern recognition

Example: Multi-Layer Perceptron (MLP)

🖼️

Convolutional Neural Networks (CNN)

Specialized for processing grid-like data such as images.

Key Components:

Convolutional Layers: Extract features using filters/kernels
Pooling Layers: Downsample spatial dimensions
Fully Connected Layers: Final classification

Important Concepts:

Local connectivity
Parameter sharing
Translation invariance

Applications:

Image classification (ResNet, VGG, Inception)
Object detection (YOLO, R-CNN)
Face recognition
Medical image analysis

Output = (Input * Kernel) + Bias

🔁

Recurrent Neural Networks (RNN)

Designed for sequential data with connections forming cycles.

Architecture:

Hidden state maintains memory
Processes sequences step by step
Shares parameters across time

hₜ = f(Wₕhₜ₋₁ + Wₓxₜ + b)

Where: hₜ = Hidden state at time t, f = Activation function, Wₕ = Hidden-to-hidden weight matrix, hₜ₋₁ = Previous hidden state, Wₓ = Input-to-hidden weight matrix, xₜ = Input at time t, b = Bias vector

Variants:

LSTM (Long Short-Term Memory): Solves vanishing gradient with gates
GRU (Gated Recurrent Unit): Simplified LSTM
Bidirectional RNN: Process sequences in both directions

Applications:

Natural Language Processing
Speech recognition
Time series prediction
Machine translation

🎭

Generative Adversarial Networks (GAN)

Two networks competing: Generator creates fake data, Discriminator tries to detect it.

Components:

Generator (G): Creates synthetic data from random noise
Discriminator (D): Classifies real vs fake data

Training Process:

D tries to maximize classification accuracy
G tries to fool D (minimize D's accuracy)
Min-max game until equilibrium

min_G max_D V(D,G) = E[log(D(x))] + E[log(1-D(G(z)))]

Where: min_G = Minimize over Generator, max_D = Maximize over Discriminator, V(D,G) = Value function, E = Expected value, D(x) = Discriminator output for real data x, G(z) = Generator output from noise z, log = Natural logarithm, z = Random noise vector

Applications:

Image generation (StyleGAN)
Image-to-image translation (Pix2Pix)
Super resolution
Deepfakes

🔄

Autoencoders

Unsupervised networks that learn efficient data encodings.

Architecture:

Encoder: Compresses input to latent representation
Bottleneck: Low-dimensional latent space
Decoder: Reconstructs input from latent code

Types:

Vanilla Autoencoder: Basic reconstruction
Denoising Autoencoder: Learns to remove noise
Variational Autoencoder (VAE): Probabilistic generative model
Sparse Autoencoder: Enforces sparsity in hidden layer

Applications:

Dimensionality reduction
Feature learning
Anomaly detection
Image denoising

🎯

Transformer Networks

Modern architecture using self-attention mechanism, revolutionizing NLP.

Key Mechanisms:

Self-Attention: Weighs importance of different positions
Multi-Head Attention: Multiple attention mechanisms in parallel
Positional Encoding: Adds sequence order information

Attention(Q,K,V) = softmax(QKᵀ/√d_k)V

Where: Q = Query matrix, K = Key matrix, V = Value matrix, Kᵀ = Transpose of K, d_k = Dimension of key vectors, √ = Square root, softmax = Softmax activation function

Architecture:

Encoder-Decoder structure
No recurrence needed
Parallel processing
Layer normalization

Applications:

Language models (GPT, BERT)
Machine translation
Text generation
Vision Transformers (ViT)

🌐

Radial Basis Function Networks (RBFN)

Uses radial basis functions as activation functions.

Architecture:

Input layer
Hidden layer with RBF neurons
Linear output layer

φ(x) = exp(-||x - c||² / 2σ²)

Where: φ(x) = RBF activation, exp = Exponential function (e to the power), x = Input vector, c = Center of RBF, || || = Euclidean norm (distance), σ = Width/spread parameter, ² = Squared

Applications:

Function approximation
Time series prediction
Classification

🔮

Self-Organizing Maps (SOM)

Unsupervised learning for dimensionality reduction and visualization.

Characteristics:

Competitive learning
Topology-preserving mapping
2D or 3D visualization of high-dimensional data

Applications:

Data visualization
Clustering
Feature extraction

Expert Level

Advanced Topics

Deep dive into sophisticated concepts and techniques

Transfer Learning

Leverage pre-trained models for new tasks, dramatically reducing training time and data requirements.

Approaches:

Feature Extraction: Freeze pre-trained layers, train only final layers
Fine-tuning: Unfreeze some layers and train with small learning rate
Domain Adaptation: Adapt model to new domain

Popular Pre-trained Models:

ImageNet models: ResNet, VGG, Inception
NLP models: BERT, GPT, T5
Multi-modal: CLIP, DALL-E

Benefits: Requires less data, faster training, better performance

Attention Mechanisms

Allow models to focus on relevant parts of input, crucial for sequence-to-sequence tasks.

Types:

Global Attention: Attend to all source positions
Local Attention: Focus on subset of positions
Self-Attention: Relate different positions in single sequence
Cross-Attention: Attend from one sequence to another

score(hₜ, h̄ₛ) = hₜᵀWₐh̄ₛ αₜₛ = softmax(score(hₜ, h̄ₛ)) cₜ = Σₛ αₜₛh̄ₛ

Where: hₜ = Target hidden state, h̄ₛ = Source hidden state, Wₐ = Attention weight matrix, ᵀ = Transpose, αₜₛ = Attention weight, softmax = Softmax function, cₜ = Context vector, Σₛ = Sum over all source positions

Regularization Techniques

Methods to prevent overfitting and improve generalization.

L1 Regularization (Lasso):

Loss = MSE + λ Σ|wᵢ|

Where: MSE = Mean Squared Error, λ = Regularization parameter, Σ = Sum, wᵢ = Weight i, | | = Absolute value

Promotes sparsity, feature selection

L2 Regularization (Ridge):

Loss = MSE + λ Σwᵢ²

Where: MSE = Mean Squared Error, λ = Regularization parameter, Σ = Sum, wᵢ = Weight i, ² = Squared

Prevents large weights, smoother models

Elastic Net:

Loss = MSE + λ₁Σ|wᵢ| + λ₂Σwᵢ²

Where: MSE = Mean Squared Error, λ₁ = L1 regularization parameter, λ₂ = L2 regularization parameter, Σ = Sum, wᵢ = Weight i

Combines L1 and L2

Gradient Problems

Common issues in training deep networks.

Vanishing Gradients:

Problem: Gradients become very small in early layers
Causes: Deep networks, sigmoid/tanh activation
Solutions: ReLU, Batch Normalization, ResNet (skip connections)

Exploding Gradients:

Problem: Gradients become very large
Symptoms: NaN values, model divergence
Solutions: Gradient clipping, proper weight initialization, lower learning rate

Residual Networks (ResNet)

Introduces skip connections to enable training of very deep networks.

y = F(x, {Wᵢ}) + x

Where: y = Output, F(x, {Wᵢ}) = Residual function (learned mapping), x = Input (identity), Wᵢ = Weights of the layers, + = Element-wise addition (skip connection)

Key Concepts:

Skip Connections: Add input directly to output
Identity Mapping: Easier to learn residual F(x)
Benefits: Train networks with 100+ layers

Advantages:

Solves vanishing gradient
Enables very deep architectures
Better gradient flow
State-of-the-art performance

Capsule Networks

Novel architecture using capsules instead of neurons to better capture spatial hierarchies.

Capsules:

Output vectors instead of scalars
Vector length = probability of entity existence
Vector direction = entity properties

Dynamic Routing:

Iterative process to determine how capsules communicate

Advantages:

Better handling of spatial relationships
Viewpoint invariance
Fewer parameters for better performance

Neural Architecture Search (NAS)

Automated method to discover optimal neural network architectures.

Approaches:

Reinforcement Learning: RL agent designs architectures
Evolutionary Algorithms: Evolve architectures over generations
Gradient-based: DARTS, differentiable search

Search Space:

Layer types and connections
Number of layers
Hyperparameters

Challenge: Computationally expensive

Few-Shot Learning

Learning from very few examples, mimicking human learning capability.

Approaches:

Meta-Learning: Learning to learn (MAML)
Metric Learning: Learn similarity metrics
Memory-Augmented: External memory mechanisms

Scenarios:

One-shot learning: 1 example per class
Few-shot: 2-5 examples per class
Zero-shot: No examples, only descriptions

Explainable AI (XAI)

Techniques to interpret and explain neural network decisions.

Methods:

LIME: Local Interpretable Model-agnostic Explanations
SHAP: SHapley Additive exPlanations
Grad-CAM: Gradient-weighted Class Activation Mapping
Attention Visualization: Show what model attends to

Importance:

Trust and transparency
Debugging models
Regulatory compliance
Identifying biases

Adversarial Training

Make models robust against adversarial attacks.

Adversarial Examples:

Small perturbations to input that fool the model

x' = x + ε · sign(∇ₓL(θ, x, y))

Where: x' = Adversarial example, x = Original input, ε = Perturbation magnitude, sign = Sign function, ∇ₓL = Gradient of loss L w.r.t. input x, θ = Model parameters, y = True label

Defense Strategies:

Train on adversarial examples
Defensive distillation
Input transformations
Certified defenses

Neural ODEs

Continuous-depth models using ordinary differential equations.

dh(t)/dt = f(h(t), t, θ)

Where: dh(t)/dt = Derivative of hidden state w.r.t. time t, f = Neural network function, h(t) = Hidden state at time t, t = Continuous time, θ = Parameters

Advantages:

Memory efficient
Continuous transformations
Adaptive computation
Normalizing flows

Use Cases: Time series, generative models, sequential data

Pruning and Compression

Reduce model size and computational requirements.

Techniques:

Weight Pruning: Remove unimportant weights
Neuron Pruning: Remove entire neurons
Knowledge Distillation: Train small model from large model
Quantization: Reduce precision (FP32 → INT8)

Benefits:

Faster inference
Lower memory usage
Deploy on edge devices
Often minimal accuracy loss

Master Neural Networks

What are Neural Networks?

Biological Inspiration

Key Characteristics

Applications

Neural Network Basics

1 The Perceptron - Building Block

Components:

2 Activation Functions

Sigmoid

Tanh (Hyperbolic Tangent)

ReLU (Rectified Linear Unit)

Leaky ReLU

Softmax

ELU (Exponential Linear Unit)

3 Weights and Biases

Weights (w)

Biases (b)

Weight Matrix Representation

Neural Network Architecture

4 Network Layers

Input Layer

Hidden Layers

Output Layer

5 Forward Propagation

Step-by-Step Process:

Key Terms:

6 Network Depth and Width

Shallow Networks

Deep Networks

Wide Networks

Training Neural Networks

7 Backpropagation Algorithm

How It Works:

Chain Rule in Action:

8 Loss Functions

Mean Squared Error (MSE)

Binary Cross-Entropy

Categorical Cross-Entropy

Mean Absolute Error (MAE)

9 Optimization Algorithms

Gradient Descent (GD)

Stochastic Gradient Descent (SGD)

Mini-Batch SGD

Momentum

Adam (Adaptive Moment)

RMSprop

10 Hyperparameters

Learning Rate

Batch Size

Epochs

Hidden Units

Number of Layers

Regularization

11 Training Techniques

Batch Normalization

Dropout

Early Stopping

Data Augmentation

Learning Rate Scheduling

Weight Initialization

Types of Neural Networks

Feedforward Neural Networks (FNN)

Architecture:

Applications:

Convolutional Neural Networks (CNN)

Key Components:

Important Concepts:

Applications:

Recurrent Neural Networks (RNN)

Architecture:

Variants:

Applications:

Generative Adversarial Networks (GAN)

Components:

Training Process:

Applications:

Autoencoders

Architecture:

Types: